Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 2

(ii) $1+i$

Express the following complex numbers in polar form:

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(ii) 1+i1+i

r=∣z∣=12+12=2 r=|z|=\sqrt{1^2+1^2}=\sqrt{2}

Since x>0x>0 and y>0y>0, θ=π4\theta=\frac{\pi}{4}.

1+i=2(cos⁡π4+isin⁡π4)\boxed{1+i=\sqrt{2}\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right)}

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